applied sciences Article Offensive and Defensive Plus–Minus Player Ratings for Soccer Lars Magnus Hvattum Faculty of Logistics, Molde University College, 6410 Molde, Norway;
[email protected] Received: 15 September 2020; Accepted: 16 October 2020; Published: 20 October 2020 Abstract: Rating systems play an important part in professional sports, for example, as a source of entertainment for fans, by influencing decisions regarding tournament seedings, by acting as qualification criteria, or as decision support for bookmakers and gamblers. Creating good ratings at a team level is challenging, but even more so is the task of creating ratings for individual players of a team. This paper considers a plus–minus rating for individual players in soccer, where a mathematical model is used to distribute credit for the performance of a team as a whole onto the individual players appearing for the team. The main aim of the work is to examine whether the individual ratings obtained can be split into offensive and defensive contributions, thereby addressing the lack of defensive metrics for soccer players. As a result, insights are gained into how elements such as the effect of player age, the effect of player dismissals, and the home field advantage can be broken down into offensive and defensive consequences. Keywords: association football; linear regression; regularization; ranking 1. Introduction Soccer has become a large global business, and significant amounts of capital are at stake when the competitions at the highest level are played. While soccer is a team sport, the attention of media and fans is often directed towards individual players. An understanding of the game therefore also involves an ability to dissect the contributions of individual players to the team as a whole.